Gemara

36b (Mishnah): Any Mitzvah that is not dependent on land applies also in Chutz La'aretz, except for Orlah and Kil'ayim;

R. Eliezer says, even Chadash (eating new grain before the Omer offering is brought) (is forbidden).

38a (Beraisa - R. Shimon): We are commanded about Orlah and Kil'ai ha'Kerem in Eretz Yisrael. The Isur of Chadash is not permanent (only until Nisan 16), it does not forbid benefit (only eating), and it is permitted (when the Omer is brought), yet it applies even in Chutz La'aretz. All the more so Orlah and Kil'ayim, which lack (two or all of) these leniencies, apply even in Chutz La'aretz!

38b (Mishnah): Chadash is forbidden mid'Oraisa everywhere. A Halachah forbids Orlah (in Chutz La'aretz). Kil'ayim is forbidden mid'Rabanan.

39a (Beraisa - R. Elazar b'Rebbi Yosi, citing R. Eliezer): Orlah does not apply in Chutz La'aretz.

Contradiction (Mishnah - R. Eliezer): Even Chadash applies in Chutz La'aretz.

Correction: The word 'even' must be deleted from the text.

Rosh Hashanah 13a: We may not offer the Omer from grain of Nochrim, for it says "Ketzirchem." Surely Bnei Yisrael offered the Omer when they entered Eretz Yisrael, for it says "va'Yochlu me'Avur ha'Aretz mi'Macharas ha'Pesach" - they did not eat until the day after Pesach (after offering the Omer).

We must say that they took grain that grew less than a third with the Nochrim.

Rishonim

Rambam (Hilchos Temidim u'Musafim 7:5): The Omer is brought only from Eretz Yisrael.

Teshuvas Rosh (2:1): All rule that Chadash applies also to grain of Nochrim. Why should it not? The opinion that Nochrim can acquire Eretz Yisrael to uproot it from Ma'aser expounds "your grain", not of Nochrim. If not for the verse, a Nochri's grain would be exempt. Regarding Chadash it says "Lechem... Lo Sochlu". This is even in Chutz la'Aretz, for it says "Moshvoseichem". Surely it applies to grain of Nochrim! Orlah applies only in Eretz Yisrael, yet it applies to what Nochrim plant. Chadash applies in Chutz la'Aretz, all the more so it applies to grain of Nochrim!

Rebuttal (Bach YD 293 DH v'Od d'Al): We cannot learn Chadash from Orlah, for Orlah is Asur b'Hana'ah and the Isur is never permitted, therefore Chachamim forbade Peros Nochrim! Also, the Rosh (Hilchos Orlah) rules that Orlah in Chutz la'Aretz is a tradition from Sinai. We may not learn a Kal va'Chomer from a tradition!

Defense (Pnei Yehoshua, Kuntres Acharon Kidushin, DH Emnam ka'Es): If Chadash applies everywhere, there is no reason to exempt grain of Nochrim. It is like any forbidden food not dependent on Eretz Yisrael. The Rosh does not learn a Kal va'Chomer, Chadash from Orlah, for this is lenient from stringent. Rather, it is a Giluy Milsa (reveals) that what applies even in Chutz la'Aretz surely applies to what Nochrim grow.

Poskim

Shulchan Aruch (YD 293:2): The Isur of Chadash applies in Eretz Yisrael and Chutz la'Aretz, both to grain of Yisrael and of Nochrim.

Bach (DH u'Mah she'Chosav Bein...): Even though most Rishonim forbid grain of Nochrim, like R. Yitzchak, our custom is to permit. Even Gedolim like the Maharshal are lenient and drink Chadash beer of Nochrim. Recently, some Chasidim are careful about this. The Yerushalmi said that the Mishnah omitted Chalah because it does not apply to (bread of) Nochrim. R. Yitzchak derived that Chadash applies to grain of Nochrim. One may not infer this! The Yerushalmi asked why the first Tana (who did not teach Chadash) omitted Chalah! R. Eliezer did not mention Chalah, lest he imply that the first Tana permits. R. Yitzchak must hold that 'even' connotes total equality. This is wrong. R. Eliezer says 'even Chadash', even though he forbids Kil'ai ha'Kerem mid'Rabanan in Chutz la'Aretz, and Chadash mid'Oraisa! We conclude that he did not say 'even'! The Rosh (Kidushin 1:62) proved from the Yerushalmi that Orlah and Kil'ayim apply to Peros Nochrim, but did not say so about Chadash. This shows that he does not rely on R. Yitzchak's proof. The Rosh wrote his Halachos after the Teshuvos. He retracted not to forbid Chadash of Nochrim, or at least was in doubt.

Bach (DH v'Od Yesh): Rosh Hashanah 13a proves that Bnei Yisrael offered the Omer after entering Eretz Yisrael, for it says "va'Yochlu me'Avur ha'Aretz mi'Macharas ha'Pesach." This implies that they did not eat until the day after Pesach. If Chadash applied to Nochri produce, why must we rely on inferences? They could not eat any grain before offering the Omer!

Rebuttal (Taz 2 and Shach 6): Perhaps they ate old grain of Nochrim. Even a Safek is permitted, for it is a Sefek-Sefeka (see Rema below). Therefore, we needed to prove that they did not eat beforehand due to Chadash. If grain of Nochrim is permitted, why did we ask only how Yisrael obtained grain for the Omer? We should have asked which grain was forbidden before the Omer! Also, the Yerushalmi about wet and dry grain forbids Chadash of Nochrim.

Bach (DH v'Chen): Terumas ha'Deshen says that Or Zaru'a forbids grain of Nochrim mid'Rabanan. He learns that it is not mid'Oraisa, like I proved, and saw that the Yerushalmi obligates, so it must be mid'Rabanan. I disproved the proof from the Yerushalmi. Since it is exempt mid'Oraisa, why should we say that Chachamim decreed? There is no source in the Gemara for this. Orlah applies to Peros Nochrim in Eretz Yisrael, therefore Chachamim forbade in Chutz la'Aretz. Chadash grain of Nochrim is exempt even in Eretz Yisrael. "Ketzirchem" disqualified grain of Nochrim for the Omer, and excludes it from the Isur of Chadash. One established to conduct with Kedushah in other ways may be stringent himself, but he may not rule to forbid Chadash of Nochrim, against the custom.

Rema (3): Stam grain is permitted after Pesach due to a Sefek-Sefeka: perhaps it is not from this year, and even if it is, perhaps it took root before the Omer. Where they surely plant oats and barley after Pesach, one must be stringent. In a place where most of the food and drink is from these grains, one should not rule stringently to others, for it is better that they be Shogeg than Mezid.

Taz (4): The Maharshal cites R. Avigdor to say that Chadash does not apply to grain of Nochrim, and Bahag connotes similarly. Perhaps they hold like the first Tana.

Rebuttal (Gra 2): The Bach holds that Chadash does not apply to grain of Nochrim. All the Acharonim refuted him.

Pnei Yehoshua (Sof Kuntres Acharon Kidushin DH ha'Din): Those who forbid Chadash mid'Oraisa in Chutz la'Aretz may not be lenient about grain of Nochrim. However, if it is mid'Rabanan in Chutz la'Aretz, grain of Nochrim is permitted.